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The equivariant universality and couniversality of the Cantor cube

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Megrelishvili M., Scarr T.

Fundamenta Mathematicae

2001

tom 167

nr 3

269-275

Let ⟨G,X,α⟩ be a G-space, where G is a non-Archimedean (having a local base at the identity consisting of open subgroups) and second countable topological group, and X is a zero-dimensional compact metrizable space. Let $⟨H({0,1}^{ℵ₀}),{0,1}^{ℵ₀},τ⟩$ be the natural (evaluation) action of the full group of autohomeomorphisms of the Cantor cube. Then (1) there exists a topological group embedding $φ: G ↪ H({0,1}^{ℵ₀})$; (2) there exists an embedding $ψ: X ↪ {0,1}^{ℵ₀}$, equivariant with respect to φ, such that ψ(X) is an equivariant retract of ${0,1}^{ℵ₀}$ with respect to φ and ψ.

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1 Fundamenta Mathematicae

1 Megrelishvili M.

1 Scarr T.

1 2001

Wyniki wyszukiwania

The equivariant universality and couniversality of the Cantor cube